Galactic Cosmic Ray Acceleration with Steep Spectra

TL;DR

This paper introduces a semi-analytic model of diffusive shock acceleration that incorporates a postcursor effect, explaining the observed steep cosmic ray spectra from supernova remnants and young radio supernovae.

Contribution

It generalizes the non-linear DSA model to include postcursor effects, producing steeper CR spectra consistent with observations.

Findings

Steeper CR spectra can be explained by the postcursor effect.

The model reproduces observed spectra of SNRs and radio supernovae.

CR energy distributions are significantly steeper than the standard E^{-2} prediction.

Abstract

Galactic cosmic rays (CRs) are accelerated by astrophysical shocks, primarily supernova remnants (SNRs), via diffusive shock acceleration (DSA), an efficient mechanism that predicts power-law energy distributions of CRs. However, observations of both nonthermal SNR emission and Galactic CRs imply CR spectra that are steeper than the standard DSA prediction, $\propto E^{-2}$. Recent kinetic hybrid simulations suggest that such steep spectra may be the result of a "postcursor", or drift of CRs and magnetic structures with respect to the thermal plasma behind the shock. Using a semi-analytic model of non-linear DSA, we generalize this result to a wide range of astrophysical shocks. By accounting for the presence of a postcursor, we produce CR energy distributions that are substantially steeper than $E^{-2}$ and consistent with observations. Our formalism reproduces both modestly steep spectra of Galactic SNRs ($\propto E^{-2.2}$) and the very steep spectra of young radio supernovae ($\propto E^{-3}$).